The Generalized Fick equations for the diffusive max flux of species $i,j_i,$ are given by:

$j_i=-D_i^{(T)}$gradlnT$+{}_i{\displaystyle \underset{j=1}{\overset{n}{}}}{D}_{ij}{d}_j,i=1,2,3$dotsn

$2$

where $D_i^{(T)}$ is the multicomponent thermal diffusion coefficient, $D_{ij}$ is the multicomponent Fick diffusivity, ${}_i$ is the mass concentration of species $i,$ and $d_j$ is the diffusional driving force for species $j.$ For a binary system, show that the equation for species A reduces to:

$j_A=-D_A^{(T)}$gradlnT$-D_{AB}{d}_A$